Electronic – How to check the Electret mic

Your sample rate must be twice the maximum frequency of interest. This is the Nyquist–Shannon sampling theorem. If you want hi-fidelity audio, your maximum frequency is the limit of human hearing, about 20kHz. Human voice is less demanding: telephone networks work up to about 3400 Hz.

You will find that the AVR's ADC isn't terribly fast, and you don't have much resources to process the data. So probably, your hardware limitations will dictate the sample rate for you.

You probably don't need to worry about codecs. A codec encodes and decodes an audio stream. A common thing to do is compress the audio for more efficient storage or transmission, but it doesn't sound like you are doing either. There are codecs that encode and decode for reasons other than compression, but I can't think of any that would be relevant here. Your computing resources are very limited on the microcontroller anyway, and you won't have much time for encoding or decoding anyway.

I'm starting to wonder whether the 1k resistors are too small, as they're smaller than the 2.2k output impedance of the microphone.

Those are the output impedance of the microphone. If you look at the mic capsule's datasheet you'll see an equivalent circuit:

I don't know why manufacturers always show the FET as a triangle. This is how it's actually configured:

So this is really a common source amplifier:

The output impedance of a common source amplifier is just \$R_\text{D}\$, the drain resistor, so when the datasheet says "output impedance (Zout) 2.2 KΩ", they really mean "output impedance of our example circuit".

With \$R_\text{S}\ = 0\$, the voltage gain of the common source amplifier is proportional to \$R_\text{D}\$, since the FET acts like a current source, so the resulting voltage is determined by V = I(FET) * Rd.

What resistor should you choose? It depends. Generally you want high gain in the first stage so you can lower the gain of subsequent stages, which lowers noise. The distortion also decreases as gain increases. You can't increase \$R_\text{D}\$ forever, though, there's a point at which current is too low and distortion increases and gain drops suddenly. Also, if your microphone is expected to pick up high SPLs, you shouldn't increase the gain too much or it will clip.

I don't know how to optimize the gain based on the parameters in the datasheet, but I'd like to know. For mass production, the gm of the FETs will vary from unit to unit (and possibly the FET type will be changed from one capsule to the next even though they have the same part number), so optimizing for maximum gain for a specific FET is probably a bad idea.